Immunoglobulin Replacement Therapy (IgRT) Versus Antibiotic Prophylaxis (PA) in Patients Treated by CD19-targeted Chimeric Antigen Receptor (CAR)T Cells for a B Cell Acute Lymphoblastic Leukemia or a B Cell Lymphoma

B cell (CD19) targeted chimeric antigen receptor modified T Cells (CAR-T) has transformed treatment of relapsed/refractory B-cell acute lymphoblastic leukemia (B-ALL) or B-cell lymphoma (BCL). Because patients receiving CAR-T often present uncontrolled disease and have undergone several lines of treatment, they may be deeply immuno-depressed and prone to infections. Hypogammaglobulinemia were reported in 74% of patients preCAR-T cells infusion (Hill JA, et al. Blood Rev. 2019 Nov). CART cells also results in depletion of normal CD19+ B cells and hypogammaglobulinemia as an on-target, off tumor toxicity. Because CAR-T cells can persist for years, patients are exposed to infectious complications secondary to long-term Bcell aplasia and severe hypogammaglobulinemia (\

Inclusion Criteria: 1. Age 16-80 years at inclusion 2. B-cell acute lymphoblastic leukemia or a B-cell lymphoma 3. With gamma globulins \=5N 4. With existing serious acute infection 5. Contraindication to immunoglobulin or to prophylactic antibiotherapy administered in this clinical trial 6. No health insurance coverage 7. Females who are pregnant or breastfeeding 8. Participation in another interventional study or being